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   "source": [
    "## 16.5 A task-scheduling problem as a matroid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 16.5-1\n",
    "\n",
    "> Solve the instance of the scheduling problem given in Figure 16.7, but with each penalty $w_i$ replaced by $80 - wi$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| $a_i$ |  1 |  2 |  3 |  4 |  5 |  6 |  7 |\n",
    "|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|\n",
    "| $d_i$ |  4 |  2 |  4 |  3 |  1 |  4 |  6 |\n",
    "| $w_i$ | 10 | 20 | 30 | 40 | 50 | 60 | 70 |\n",
    "\n",
    "$\\langle a_5, a_4, a_3, a_6, a_7 \\rangle$, $w_1 + w_2 = 30$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 16.5-2\n",
    "\n",
    "> Show how to use property 2 of Lemma 16.12 to determine in time $O(|A|)$ whether or not a given set $A$ of tasks is independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inserting by deadline."
   ]
  }
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